Recent content by Highwind

Hi, I search for the maximum of a quadric for points on a sphere. I have an affine transform A (4x4 matrix, in homogeneous coord.) and apply it to points on (and inside) a sphere x \in S_{m,r} \Leftrightarrow (x-m)^2<=r^2 . (Although I think the extremum must be on the surface of the sphere?)...

yes, einstein says that space-time is curved. But still the universe might be of torodial shape (not necessarily flat).

Yes, thanks. Now it's clear. If you actually take the parametrization f(u,v) = (cos u, sin u, cos v, sin v) you can easily calculate the first and second fundamental tensor (being the unity matrix). Therefore the surface is flat. Now only the question if the universe is a 3 dimensional torus...

I understand what you're at. I also think that it is true, but the only gap in the argumentation is this: You take a circle (having constant curvatrue) and another circle (also having constant curvature) in another R^2. Why exactly has the product of those circles (in the product of those...

Your argumentation is not completeley clear: Why exactly do you think that an embedding in R^4 can be found with constant gauss curvature? When I take the product of the two S^1 (circles) I can easily embedd the result (namely the torus) in R^3 (as a doughnut). This is of course also a valid...

hi, for most of you this might be a simple question: Is it possible to embed the flat torus in Euclidean space? If we, for example, take a rectangle and identify the left and the right sides we get a cylinder shell, that can be embedded easily in R^3. If we construct the...